Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure

被引：0

作者：

Bai, Xiang ^{[1
]}

Tan, Changhui ^{[2
]}

Xue, Liutang ^{[3
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

[3] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, MOE, Beijing 100875, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 407卷

关键词：

Euler-alignment system; Fractional diffusion; Global well-posedness; Asymptotic behavior; Optimal decay; rates; LARGE-TIME BEHAVIOR; UNIDIRECTIONAL FLOCKS; EQUATIONS; EXISTENCE; REGULARITY; DYNAMICS; STABILITY; SPACES;

D O I：

10.1016/j.jde.2024.06.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent behaviors for the system, providing time decay estimates with optimal decay rates. Notably, the optimal decay rate we obtain does not align with the corresponding fractional heat equation within our considered range, where the parameter alpha is an element of (0, 1). This highlights the distinct feature of the alignment operator. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：269 / 310

页数：42

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